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 A005284 Number of permutations of (1,...,n) having n-6 inversions (n>=6). (Formerly M4178) 5
 1, 6, 27, 111, 440, 1717, 6655, 25728, 99412, 384320, 1487262, 5762643, 22357907, 86859412, 337879565, 1315952428, 5131231668, 20029728894, 78265410550, 306109412100, 1198306570554, 4694809541046, 18407850118383 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,2 COMMENTS Sequence is a diagonal of the triangle A008302 (number of permutations of (1,...,n) with k inversions; see Table 1 of the Margolius reference). - Emeric Deutsch, Aug 02 2014 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.14., p.356. R. K. Guy, personal communication. E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 6..1000 B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4. R. H. Moritz and R. C. Williams, A coin-tossing problem and some related combinatorics, Math. Mag., 61 (1988), 24-29. FORMULA a(n) = 2^(2*n-7)/sqrt(Pi*n)*Q*(1+O(n^{-1})), where Q is a digital search tree constant, Q = 0.2887880951... (see A048651). - corrected by Vaclav Kotesovec, Mar 16 2014 EXAMPLE a(7)=6 because we have 2134567, 1324567, 1243567, 1235467, 1234657 and 1234576. MAPLE g := proc(n, k) option remember; if k=0 then return(1) else if (n=1 and k=1) then return(0) else if (k<0 or k>binomial(n, 2)) then return(0) else g(n-1, k)+g(n, k-1)-g(n-1, k-n) end if end if end if end proc; seq(g(j+6, j), j=0..30); # Barbara Haas Margolius, May 31 2001 MATHEMATICA Table[SeriesCoefficient[Product[(1-x^j)/(1-x), {j, 1, n}], {x, 0, n-6}], {n, 6, 25}] (* Vaclav Kotesovec, Mar 16 2014 *) CROSSREFS Cf. A008302, A000707, A001892, A001893, A001894, A005283, A005285, A048651. Sequence in context: A216263 A003517 A108958 * A198694 A220101 A014825 Adjacent sequences:  A005281 A005282 A005283 * A005285 A005286 A005287 KEYWORD nonn AUTHOR EXTENSIONS More terms, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), May 31 2001 Definition clarified by Emeric Deutsch, Aug 02 2014 STATUS approved

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Last modified January 18 09:24 EST 2019. Contains 319269 sequences. (Running on oeis4.)